Quantum Units and Angular Numbers
Everything is Packaged in Quantum Units
Everything in the Universe comes in packages (quantum units), large or small. Everything comes in a fixed range of sizes from one extreme, where it is never found in a smaller size; to the other extreme, where it is never found in a larger size. This applies to eggs, oranges, dogs, cats, men, women, and even stars in the heavens, etc. These larger packages or quantum units, can always be broken up into smaller elementary quantum units. It is useful to enumerate what some of these smaller units are. We will list them like this:
So everything is made up of varying numbers of the same type of "bricks", but in varying sizes and varying geometric shapes.
Some Factors that Determine the Size of an Object
The actual size of an object is determined by the forces acting on the object. We find that all living cells, depending on what type they are,
vary little from a certain average size, and no cell can grow larger than a certain absolute magnitude. Some factors that can limit their size are: gravity, surface tension, heat, light, etc. It has also been shown that there is a limit to the amount of cytoplasm that can surround a living nucleus, and that the nucleus itself has a limitation to its size.
One of the factors limiting the size of a human body is the circulatory system, which can keep the body warm or cool only within certain size limitations. Another factor limiting size is the ability of the bones and muscles to support the body weight against the force of gravity. Beyond a certain absolute size, the body would become immobile, or the supporting structure of bones and muscle would collapse.
In a similar manner, the stars are also found to be limited to a certain size range. It is a surprising fact that the mass of stars and even nebulae all fall within the average range of 10 to the tenth power of grams of matter per star. Gravitation draws matter in towards the star center, but the radiation outward is an opposite force leading to the disintegration of the star. The two forces approximately balance each other to keep the amount of matter in the average range while the star is in existence.
Some Factors Determining the Quantum Sized Vortex on a Surface Weather Map
In the face of all the evidence throughout the Universe that most things come in packages, large or small, it would be surprising if weather vortexes did not show a minimum size limit and that larger sized highs and lows would be multiples of the minimum or quantum sized vortex. One of the factors for the limiting quantum size of a high or low would certainly be linked to the depth of the atmospheric layer of air (which varies with the temperature among other reasons). We must keep in mind that the temperature of a column of air (and the subsequent depth of the atmosphere) varies greatly from winter to summer, and from polar regions to the equatorial zone. You may recall from Chapter 4, that Benard found the diameter of the cells to be approximately 3 times their depth, so that if the depth of the liquid varied, the cells diameters also varied.
The surface of the Earth is completely covered every day with highs and lows-the total number must always be a whole, rational number, since there is no such thing as a part of a high or low. The smallest high
or low on a surface hemisphere map (above the equatorial belt at any given point in time could be considered as the elementary quantum unit. Any other high or low on the map would be of a size that is equal to, or 2, 3, 4, 5, etc., times as big as the fundamental vortex. If a map were to be magnified and drawn showing more detail than is shown on the hemispheric map, you would find in many situations, a group of tiny vortexes instead of one single large vortex. The single large vortex that is shown on the map, in this case, is the center around which the other vortexes cluster. Every other vortex center that is stationed in any other location on the Earth will react to the effects of the cluster of vortexes as if it were indeed, a lone vortex with only one center; since the air is generally rising upwards over the whole area of the cluster. So we would find that there would be a whole number of smaller sized quanta units inside the single main vortex-in the same manner as molecules being made up of atoms, and they in turn, being made up of protons, electrons, and neutrons. Smaller sized units (too small to be shown on a hemispheric polar stereographic map) can break the minimum sized units that are actually drawn on the polar stereographic map into 2, 3, 4, 5, etc., parts, exactly, depending on the situation. I do not consider it unreasonable to say that this process of subdividing larger units can be continued right on down to the spacing of clouds.
The concept of a minimum quantum size for vortexes has been very useful to me in my investigations and has been one of the theoretical underpinnings that helped me develop the charts that you will soon be looking at (if you haven't already). The concept of quantum sized vortexes, is necessary in explaining some features of the charts, but is not vital to the use of the charts, which show the spatial arrangement of vortexes (regardless of size).
Some further thoughts on the quantum principle. Oranges can grow from a tiny size to a nice fat, juicy shape. Likewise, a high or low can grow from a tiny disturbance of a few miles (or even smaller), to one
that stretches for thousands of miles. The principle of quantum size, as I visualize it, is that there are preferred sizes for a given vortex. If the vortex is not a quantum size, then it will change very rapidly (by pulses of growth or decay) to the next higher or lower quantum size (which can be 1, 2, 3, etc., times the basic quantum unit). This reminds us of the Chladni plates where the sand slid rapidly to the nodal positions when the plate was vibrated.
"Diffraction Grating" for Finding the Quantum Vortex and also for Exposing Simple Geometric Conffgurations
Wave numbers can be thought of as wave lengths or wave distances, since we are breaking a circumference up into a certain number of parts when we calculate wave number. Each part of the circumference represents an actual distance. When converting wavenumbers into distances on a polar stereographic map, we express the distance in degrees of latitude. One degree of latitude always represents the same distance of 60 nautical miles anywhere on the map. We don't use degrees of longitude to measure distance, because distance between any two longitude lines varies when going from the pole to the equator.
When we look at the weather map for 7 December 1950, we find that the closest distance between any two vortexes (high or low) is in the range of approximately 3.75 degrees of latitude. Vortex centers #83 and #84 are separated by approximately 3° (see the Identification map, pg 109); while #66 is 4.3° from #65, and 4.1° from #67. We see that the vortexes represented by points #65, #66, #67 do not look like closed circular shapes as drawn on the map. There should be no confusion for those readers who have little acquaintance with weather maps, since every high or low of any size, always has a closed circular type of pattern, even though a map may not show all the fine details. A more detailed description of the charts is given in the next chapter. I have found that the 3.75° distance is the smallest quantum unit of spacing between any two vortex centers in the winter season (since fundamental sizes may possibly vary with changes in temperature).
In 1912, Max Laue (1879-1960) came to the conclusion that X-rays were really very short light waves, and the length of the light waves was in the same range as the distance between the atoms in a crystal.
Friedrich and Knipping carried out the experiment which showed that Xrays are waves and crystals are regular arrays of atoms spaced at equal distances apart. They developed a tool that measured the distance between the atoms, which at the same time served to measure the length of the light wave. This tool is the wellknown diffraction grating, which is a system of close, equidistant, parallel lines ruled on a polished surface. Laue suspected the spacing of the atoms in advance; he said that the wavelength of X-rays would fit neatly into the spaces between the atoms.
Since the closest spacing between any two vortex centers is in the neighborhood of 3.75°, we have a clue as to what wavelength to use for making a tool (similar in principle to the diffraction grating) for analyzing the angular separation between 3 or more vortex centers and the radial spacing between centers. I have found that the use of 1.875° (half of 3.75°) will give greater detail, since half the distance between any two vortex centers can be considered as the radial distance of each of the vortexes in the direction of the line joining them. See Figure 10-1.
If we divide the 360° circumference of a circle by 1.875°, we get a wavenumber of 192. Table VI gives the value in degrees of each of the 192 divisions. We note that the angles of 30°, 60°, and 120° (and their submultiples) occur in this table and also the angles of 45°, 90°, and 180° (and their submultiples). These, of course, are the angles that occur in triangular, square, and hexagonal conffgurations, as can be seen in Figures 10-2 through 10-6. The occurrence of these angles on a weather map would be one of the indications that a regular geometric shape exists.
Figure 10-2 shows three imaginary vortexes arranged in a triangular formation. We will find the angles of 60° prevailing between their centers when they are in an equilibrium position with regard to each other.
Next, we will look at angles formed by the centers of four regularly arranged vortexes. There are two ways in which four vortexes can come together, as shown in Figure 10-3. In Figure 10-3a, we find the angles of 90° and 45° predominating, while in Figure 10-3b, we find the angles of 60° and 120° predominating, which is the stable condition.
If we have a nuclear or central vortex, we find that there are two general arrangements possible, as in Figure 10-4. In 10-4a, we find an extension of the square formation (Figure 10-3a) with the angles of 90°
and 45° predominating. And in 10-4b, we have the nuclear hexagonal arrangement with the angles of 120° and 60° predominating.
In Figure 10-5, we show the arrangement of 5 vortexes in a pentagonal form.
There are many permutations and combinations possible, but I will show one more common configuration in Figure 10-6, which shows a variation of 4 vortexes in a formation, but with 4 other vortexes nesting around them. The predominant angles are still 90° and 45°.
Construction of the Weather Tool
After this diversion into angular formations, we now turn to the actual construction of a tool that can be used on a weather map. See
Figure 10-7 for a reduced view of the tool, which is a protractor covering the full 360° circle with the unique feature of being divided into sectors that are all equal to 3.75°. The angle of 1.875° has been chosen as the harmonic element to test for resonance. The reason for using the 3.75° spacing, instead of the 1.875° spacing, is that it reduces the clutter of too many lines, especially near the center.
Figure 10-7. A view of the "diffraction" tool used to construct the charts in this book.
This tool, consisting of a transparency, may seem disarmingly simple. The unique feature, as you wilI shortly see, is that it is a "diffraction grating", or "tuning fork", if you please, for the weather map. If I did not introduce this tool, you would find the examples I show in the succeeding pages to be intriguing, but you would be baffled if you attempted to duplicate the results. You would wonder how the accuracy shown could be obtained with the commonly available protractor.
Other Possible Weather Tools
There are other types of "diffraction gratings" that can be constructed for a weather map if we use a different wavelength. If we
use a minimum wavelength of 2.25°, we get a wavenumber of 160. Table VII gives the value in degrees of each of the 160 divisions. In this table, we note the angles of 36°, 72°, 108° and all their submultiples. These are the angles that occur in pentagonal configurations. We also find the angles of 22.5° and 180° etc., which also occur in Table VI.
If we use still another minimum wavelength of 2.8125°, we get a wavenumber of 128 for 360°. Table VIII gives the value in degrees of each of the 128 divisions. In this table, we ffnd the angles of 45°, 90°, 180°, and their submultiples.
Upon examination, we find that many of the angles in Table VI also appear in Table VII, but more of them appear in Table VIII. The angles of Table VII are the angles associated with the pentagon. While there undoubtedly are some pentagonal formations present to help fill the space on the surface of the hemisphere, they are not as numerous as the common space fillers, such as the hexagon, the equilateral triangle, the square, and their various manifestations and complications.
We will shortly make an analysis of the weather at 1230 G.M.T. on 7 December 1950, in which we consider 104 disturbances, large and small, occurring in the Northern Hemisphere. There are many smaller or obscure disturbances occurring over the hemisphere that have not been entered or considered, due only to lack ofaccurate data with which to make calculations. All 104 (and the additional ones that are not analyzed) are like players in a symphony orchestra, each with his or her own instrument. How do we bring order out of the large array of waves that are being generated simultaneously? We use the principles of harmonic analysis--not statistics.
The 1.875° angle is used in two ways: First, as the harmonic element to test for resonance with other vortexes along the radial distance outward from a vortex; and second, along the circumference of any appropriate circular ring. Refer back to Figure 9-4, for a visual picture. The use of the other two harmonic elements shown in Table VII and Table VIII (or others that may come to mind) would expose formations of interest, but they are not shown to keep this book from becoming too fat
and monstrous. Keep in mind, one of the main purposes of this first book is to establish, beyond any doubt, that there is an undreamt of order in the arrangement of all the features on a surface weather map. Order of a magnitude that no one in the field of meteorology thought was even possible, and would certainly seem difficult to prove with an ordinary surface weather map that was drawn prior to the advent of computers and satellites. The charts I show in this book can only give a glimpse of a few of the "beasts" that almost seem alive as they roam about the surface of the Earth to give us the weather we experience.